1. Field of Invention
The present invention is directed toward the field of x-ray diffraction as a versatile tool to determine the structure of atomic and superlattice systems with preferred orientation along at least one dimension. The invention may be configured for the determination of structure in lipid membranes, in-situ thickness measurements of thin films during growth, and determination of lattice mismatch in epitaxial crystalline films.
2. Description of the Prior Art
X-Ray diffraction has been used to measure in situ thickness of thin films during deposition (Luken, et. al., SPIE Vol. 2253:327 (1994)). Luken et al. describe an angle dispersive x-ray reflectometer which employs a Johansson-type (T. Johansson, Zeit. Physik, 82:507 (1933)) curved crystal monochromator to focus and wavelength-select X-radiation, with a convergence angle of 2.5.degree. (4.4.times.10.sup.-1 radians), down to a silicon substrate surface on which a W/Si multilayer is grown. The Johansson-type crystal is one in which the reflecting surface is ground to a radius of curvature 2R and the crystal is subsequently bent to a radius of curvature R. The low angle x-ray reflectivity is monitored from the Si substrate simultaneously between 0.degree. and 2.5.degree. using a linear position sensitive charge-coupled device (CCD) detector. The authors used the instrument to monitor the growth of the multilayer in-situ during evaporative deposition.
While in principle, the Johansson crystal provides "perfect" point-to-point focusing, there are limitations to using Johansson crystals. For example, the size of the beam at the focus is approximately the same size as the source. For a fine focus x-ray source, with a target source size of 0.4.times.8 mm.sup.2, this dimension at a 6.degree. (0.10 radians) takeoff angle is defined by (0.4 mm)Sin(0.10) and has a value of about 42 .mu.m in the focusing plane. To further reduce the focus, the effective source size would need to be reduced with a slit to block part of the radiation. Not only would the use of a slit diminish the intensity of the x-ray beam, but alignment is now made considerably more difficult, since the monochromator and the sample need to be positioned to within microns with respect to the source in order to take advantage of the small focus. Furthermore, because the crystal monochromator surface must be ground and bent to a very specific curvature, there is, for practical purposes, no forgiveness built into the design to compensate for misalignments or bending error. Thus, the requirement that the surface be ground and then bent makes the fabrication expensive.
Small angle x-ray scattering has been used to measure structure in oriented lipid bilayers (Mason and Trumbore, Biochemical Pharmacology 51:653 (1996)). Using small-angle x-ray spectrometry, Mason and Trumbore report the sensitivity of the method to indicate the incorporation and location of antioxidants into the lipid matrix. To achieve the orientation, multilayer stacks of the lipid bilayers are centrifuged down onto a flat substrate from vesicles suspended in an aqueous medium. The lipids are found to align spontaneously with the stacking axis normal to the substrate surface. The substrate is made from a bendable sheet of aluminum which is subsequently mounted on a curved glass surface (radius of curvature c.a. 20 mm). An incident x-ray beam is then focused with a bent grazing incidence mirror to illuminate the curved substrate with an intense beam of small, but unspecified, angular divergence. Different parts of the incident beam intersect the curved surface at different angles of incidence, and the scattering from the entire beam is measured on a position-sensitive x-ray detector which measures the intensity as a function of linear position along the detector axis. The discrete diffraction peak intensities are then Fourier transformed to determine the electron density profile within the lipid bilayer. Mason and Trumbore report the difference in electron density between the oriented lipid lamellar stack incubated in the vesicle state without antioxidant and the same lipid incubated with the target antioxidant in the vesicular suspension before centrifugation.
While this method is able to capture all the relevant diffraction information, the technique suffers from the time-consuming step of gluing the aluminum substrate to the curved glass surface. Furthermore, the x-ray beam is not monochromatic, but is simply filtered to significantly reduce the K.sub..beta. radiation. The dominant radiation which diffracts from the sample is the K.sub..alpha.1 /K.sub..alpha.2 doublet. The continuous brehmstrahlung background radiation, particularly at energies between 4 and 8 keV, remains. This continuous spectrum radiation increases the background signal on top of which the diffraction peaks are observed and this subsequently diminishes the ability to observe weak diffraction lines and accurately determine integral peak areas.
High resolution, wide angle x-ray scattering is commonly used to determine the lattice parameters in epitaxially grown films (in particular, strained-layer superlattices) with respect to the lattice of the single crystal substrate. The typical approach is to employ a two-crystal spectrometer (monochromator and sample) and measure a rocking curve of the sample in the vicinity of a Bragg diffraction angle from the sample substrate. These angles are typically in the range of 30.degree. to 50.degree. and the rocking curve scan is performed over a range of several degrees. During the rocking scan, the diffraction intensities are measured using a scintillation detector with an entrance slit large enough to accept diffraction over an angular range of several degrees. The wide detector slit precludes the ability to know the diffraction angle precisely. As a result, satellite peaks and orientation of reciprocal lattice vector in strained-layer superlattices are not readily discernible.
Picreaux et al. (Semiconductors and Semimetals, 33:139 (1991)) employ a linear position-sensitive x-ray detector (PSD) to measure diffraction intensities from epitaxial films in rocking curve scans with a high resolution two-crystal x-ray spectrometer. While the use of the PSD provides information to allow reciprocal space mapping of the epitaxial layers, the method still requires illumination of the substrate with a highly collimated, monochromatic beam and then measuring the diffraction intensities while step scanning the sample tilt one angle at a time; this approach is both complicated and time-consuming.
Using a high resolution, two-crystal x-ray spectrometer, Tsuchiya et al. (Proc. 4th Indium Phosphide and Related Materials Conf., Newport, R.I., 1992) describe feedback control used to adjust the growth conditions during deposition of a vapor phase epitaxial grown film of InGaAs on a single crystal substrate, InP. A scintillation detector with a wide slit was used and the entire x-ray source and monochromator optics were rotated about the sample in order to perform the rocking curve scans. While this method demonstrates the feasibility of using x-ray diffraction for deposition feedback, rotation of the x-ray source about the sample is cumbersome and limits the amount of space available for the deposition system. Furthermore, the method is impractical for faster deposition, since the incident angles are stepped one at a time.
X-rays may be simultaneously focused and monochromatized by reflecting a divergent x-ray beam from a curved single crystal such that incident beam intersects the crystal at the Bragg diffraction angle for the desired wavelength. An ideal shape for such a focusing x-ray monochromator is for the crystal curvature to be identical with a logarithmic spiral. DeWolff (Selected Topics on X-Ray Crystallography, Ch. 3, ed. J. Bouman, North-Holland, Amsterdam, 1951) describes a four-point crystal bender to approximate the ideal logarithmic spiral form for a focusing monochromator crystal to second order with respect to the local crystal curvature. This monochromator design has been employed for almost half a decade in powder diffraction spectrometers. The bending design is simple, robust, and in contrast to the Johansson-type focusing, the logarithmic spiral does not require a true point x-ray source.
The main disadvantage of this type of focusing monochromator is that the focusing quality can not be improved beyond that already accomplished with the conventional four-point bending apparatus. This inherent limitation is due to the difference in functional form between the ideal logarithmic spiral and the shape that the monochromator can assume in a mechanical, four-point bending apparatus.
X-rays are totally reflected from smooth mirror surfaces when the x-rays illuminate the mirror below a grazing incident critical angle. For hard x-rays (&gt;1 keV), this angle is typically on the order of a few tenths of a degree. Underwood and Turner (SPIE, 106:125 (1977)) describe how bent, nondiffracting mirror surfaces can made to focus or collimate x-rays more efficiently by grinding the sides of the mirror such that the width of the reflecting surface varies as function of the length. This shaping procedure is used to "tune" the moment of inertia as a function of length, and allows a bending system to more accurately define the shape of the mirror to the ideal parabola or ellipse. The authors intended this design to be used in astrophysical applications for x-ray telescopes; and these mirror focusing elements differ significantly from diffracting crystal optics.
Thus, there remains a need for an x-ray spectrometer with a curved crystal monochromator which can provide improved point focusing of the x-ray source and micron scale scanning of the sample surface. There is a further need for methods of preparing curved crystals having a curvature of a logarithmic spiral which overcome the inherent limitations of the prior art.